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Q7. A small open rectangular box is to be fabricated from a square sheet of steel of side 20 cm, by cutting congruent squares from each comer and bending the edges up which are then welded along the comer joints.

Given that the volume of the box has to be maximised, calculate EACH of the following:

(a) the side length, using differential calculus, of the square to be cut from each comer; (12)

(b) the volume of the box; (2)

(c) the external surface area of the box. (2)